# Exponential

a^x

general exponential increase ~ the effects are cumulative

e^x

natural exponential increase ~ every step has immediate and cumulative effects

— Me@2014-10-29 04:44:51 PM

# Market price 3

Sometimes, a higher price may be good for your customers, for you can provide more time for the technical support to them.

— Me@2014-10-28 10:50:58 AM

# 語言科目

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（TK: 通常，最勁（厲害）的人，都是讀數學出身的。彷彿只要數學勁，就幾乎什麼行業，都可以做得到。）

「宇宙人語言」的意思是，在宇宙中的任何一個角落，一加一都是等於二。無論你移居去哪一個星球，你也不用擔心，你已學的數學知識，不再適用。數學可以說是，應用範圍取廣的知識。

— Me@2014.10.29

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paradox ~ mixing a level with its meta-level

There is no mixing-level problem for the equation

f(x) = x,

because it just means that two variables have the same value. In other words, the value of a function of x is equal to the value of x.

However, for the equation

f = x,

there is a mixing-level problem, resulting no meanings; because

the equation means that a function (aka a formula of a number) is equal to a variable (aka a number).

A formula of a number is a structure. It cannot be a number.

— Me@2013-07-16 10:45 AM

— Me@2014.10.11

# Cartesian Dualism

In philosophy of mind, dualism is the position that mental phenomena are, in some respects, non-physical, or that the mind and body are not identical. Thus, it encompasses a set of views about the relationship between mind and matter, and is contrasted with other positions, such as physicalism, in the mind–body problem.

— Wikipedia on Dualism (philosophy of mind)

The mind–body problem in philosophy examines the relationship between mind and matter, and in particular the relationship between consciousness and the brain.

The problem was famously addressed by Rene Descartes in the 17th century, resulting in Cartesian dualism, and by pre-Aristotelian philosophers, in Avicennian philosophy, and in earlier Asian traditions. A variety of approaches have been proposed. Most are either dualist or monist. Dualism maintains a rigid distinction between the realms of mind and matter. Monism maintains that there is only one unifying reality, substance or essence in terms of which everything can be explained.

— Wikipedia on Mind–body problem

2014.10.10 Friday ACHK

# Pattern 2

pattern ~ redundant information

— Me@2011.05.08

have a pattern

~ can be compressed

— Me@2014.10.04

# 背誦量

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（TK: 運算機會率題目時，如何提升準確度？）

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（TK: 其實我是有背的，但是，時常也誤中副車，差一點才能想中正確方法。）

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「背」的意思並不是說，你把「魔法筆記」，由頭至尾，閱讀一次就算。「背」的真正意思是，要你做到「過目不忘」，即是，在平日做練習，或者考試時，你都可以在心裡翻查，筆記上的每一頁，每一個細節。

— Me@2014.10.05

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# Heisenberg

My first query is why does he claim the position and period of an electron to be unobservable “in principle”? There was theoretically no reason (at THAT time) to doubt that these quantities could be measured, though certainly they were indeterminate practically.

Werner Heisenberg obviously disagreed with this assumption of yours and it just happened that his ability to disagree made him a founder of quantum mechanics.

He has spent several years by trying to develop “quantized planetary” models of the helium atom etc. before he understood that this failing project is failing for fundamental reasons. Such a helium with well-defined positions would be described by a chaotic 3-body problem and there would be no way how it could be consistent with the known regular behavior of the helium atom (and other atoms and other coherent systems), including the sharp spectral lines.

So Heisenberg was able to see in 1925 something that you can’t see now: that the electrons can’t be going along any particular trajectories while they’re in the atoms. Instead, what is observed is that they have a totally sharp energy from a possible list, the spectrum – something we can really observe via the photons that atoms emit or absorb. To conclude that electrons can’t be going along particular classical trajectories in the atoms, he didn’t have to wait for measuring apparatuses that would be sufficiently accurate. He was able to make this conclusion out of the available data by “pure thought”, and he was right.

— Lubos Motl

2014.10.04 Saturday ACHK

# Control

Release 2

Anything you try to control will collapse.

Let go and release your potentials.

— Me@2011.07.24

# 天人天書 1.2.1

（安：你彷彿收集了很多「神作」。你最初是怎樣知道，那些「神作」的存在？）

（安：但是，可以叫做「神作」，即是十分難得。換句話說，遇到的機會率較微。間中給你遇到一兩本「神作」，並不出奇。但是，你好像遇見過，大量的「神作」。那就十分奇怪。）

— Me@2014.10.02